ANTI-SIMPSON'S QUADRATURE FORMULA AND ITS EXTENSION FOR EVALUATION OF ELLIPTIC AND OTHER INTEGRALS IN ADAPTIVE ENVIRONMENT
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 34
DOI: https://doi.org/10.56827/SEAJMMS.2024.2002.33
Author :
Debasish Das (Department of Mathematics, Bhadrak Autonomous College, Bhadrak, Odisha, INDIA)
Sanjit Kumar Mohanty (Department of Mathematics, B.S. College, Jajpur - 754296, Odisha, INDIA)
Litan Kumar Barikee (Department of Mathematics, SOA University, Bhubaneswar, Odisha, INDIA)
Rajani B. Dash (Department of Mathematics, Ravenshaw University, Cuttack, Odisha, INDIA)
Abstract
We have constructed an anti-Simpson's quadrature formula using Simpson's $\frac{1}{3}rd$ quadrature formula following the idea given by D. P. Laurie. An extension of this formula is developed by taking average linear combination with the Simpson's $\frac{1}{3}rd$ quadrature formula. Through error analysis, we studied the theoretical dominance of this extended anti-Simpson's quadrature formula over its constituents. We accomplished numerical verification of the formula evaluating test integrals including elliptic ones. We depict the novelty of the formula in both non-adaptive and adaptive environments. In adaptive environment the dominancy of the rule over its constituents clarifies both in number of steps and error committed.
Keywords and Phrases
Simpson's $\frac{1}{3}rd$ quadrature formula $(Q_{S_{3}}(f))$ , Anti-Simpson's 4-point quadrature formula $(Q_{aS_{4}}(f))$ , Extended anti-Simpson's quadrature formula $(DS_1(f))$ , Adaptive integration scheme, Elliptic integrals.
A.M.S. subject classification
Primary 65D30, 65D32, Secondary 65E05, 65A05.
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